Nonlinear and stimulated effects in resonance fluorescence of one and two atoms

The Stark representation of the resonator field and the first order of perturbation theory of the fluorescence field are used to study the fluorescence spectrum of one and two two-level atoms in an ideal resonator as a function of the initial excitation of the system. It is shown that in the absence of resonator photons (n_c=0) the spectrum obtained for initial excitation of one atom consists of two lines located symmetrically relative to the central frequency ω_α. In all other cases the spectrum consists of the central harmonic ω_α and of ω_α±2Ω satellites (Ω is the Rabi frequency). The intensity of collective higher harmonics ω_α±4Ω is low and it falls on increase in the resonator field as 1/n_c². The nonlinearity of the interaction Hamiltonian results in parametric amplification of the ω_α+2Ω harmonics and in attenuation of the ω_α—2Ω harmonics. In the case of two atoms it is possible to achieve stimulated fluorescence at the harmonics ω_α±2Ω.